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Category: Algebra

find-all-subgroup-of-Z-7-

Question Number 158537 by apriadodir last updated on 05/Nov/21 $$\mathrm{find}\:\mathrm{all}\:\mathrm{subgroup}\:\mathrm{of}\:\left(\mathrm{Z}_{\mathrm{7}} ,+\right)\: \\ $$ Commented by mkam last updated on 06/Nov/21 $${since}\:{Z}_{\mathrm{7}} \:{is}\:{a}\:{prime}\:{group}\:{then}\:{the}\:{sup}\:{group} \\ $$$${is}\:{a}\:{non}\:{trivial}\:{group}\:{z}_{\mathrm{7}} \:{and}\:\left\{\mathrm{0}\right\}…

Prove-that-a-2-tan-k-x-b-2-sin-k-x-gt-2abx-k-for-all-x-0-pi-2-and-positive-integer-k-

Question Number 158534 by HongKing last updated on 05/Nov/21 $$\mathrm{Prove}\:\mathrm{that}\:\:\:\mathrm{a}^{\mathrm{2}} \mathrm{tan}^{\boldsymbol{\mathrm{k}}} \mathrm{x}+\mathrm{b}^{\mathrm{2}} \mathrm{sin}^{\boldsymbol{\mathrm{k}}} \mathrm{x}\:>\:\mathrm{2abx}^{\boldsymbol{\mathrm{k}}} \\ $$$$\mathrm{for}\:\mathrm{all}\:\:\mathrm{x}\in\left(\mathrm{0}\:;\:\frac{\pi}{\mathrm{2}}\right)\:\mathrm{and}\:\mathrm{positive}\:\mathrm{integer}\:\boldsymbol{\mathrm{k}} \\ $$$$ \\ $$ Terms of Service Privacy Policy…

n-1-n-1-3-1-n-1-3-1-

Question Number 158528 by amin96 last updated on 05/Nov/21 $$\underset{\boldsymbol{\mathrm{n}}=\mathrm{1}} {\overset{\infty} {\prod}}\left(\frac{\left(\boldsymbol{\mathrm{n}}+\mathrm{1}\right)^{\mathrm{3}} −\mathrm{1}}{\left(\boldsymbol{\mathrm{n}}+\mathrm{1}\right)^{\mathrm{3}} +\mathrm{1}}\right)=? \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com

if-x-y-z-gt-0-and-xyz-27-prove-that-1-x-2-27-1-y-2-27-1-z-2-27-1-12-

Question Number 158508 by HongKing last updated on 05/Nov/21 $$\mathrm{if}\:\:\mathrm{x};\mathrm{y};\mathrm{z}>\mathrm{0}\:\:\mathrm{and}\:\:\mathrm{xyz}=\mathrm{27}\:\:\mathrm{prove}\:\mathrm{that}: \\ $$$$\frac{\mathrm{1}}{\mathrm{x}^{\mathrm{2}} +\mathrm{27}}\:+\:\frac{\mathrm{1}}{\mathrm{y}^{\mathrm{2}} +\mathrm{27}}\:+\:\frac{\mathrm{1}}{\mathrm{z}^{\mathrm{2}} +\mathrm{27}}\:\leqslant\:\frac{\mathrm{1}}{\mathrm{12}} \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com

x-3-5x-3-2-x-1-

Question Number 27419 by ayushrtet last updated on 06/Jan/18 $$\left({x}^{\mathrm{3}} +\mathrm{5}{x}^{\mathrm{3}} −\mathrm{2}\right)/\left({x}−\mathrm{1}\right) \\ $$ Answered by Rasheed.Sindhi last updated on 06/Jan/18 $$\left({x}^{\mathrm{3}} +\mathrm{5}{x}^{\mathrm{3}} −\mathrm{2}\right)/\left({x}−\mathrm{1}\right) \\…